This place is introduced in the second episode, where JH goes after spending the evening with his friends DC and HI. However, he is not alone. HI followed him there.

JH teased HI so that the latter ran after him. This place is also mentioned in JH’s application letter which makes CSH curious, therefore she goes there on her own.

However, she is caught by JH who is so happy because this gives him the opportunity to approach her. In his letter, JH described this place as his place of retreat, even CSH could feel that he treasured it very much therefore she wanted to see it with her own eyes. Curiosity and her experience with JH in Cuba were the reasons why she went there. After the scandal is revealed, HI and JH are seen again at the playground.

She asks him about the photo. As we can see, HI also knows the importance of this place. She knew what JH would do after seeing his picture in the internet. After revealing his identity due to the anonymous post, JH goes to the playground in order to think and gather some strength. He is not sure if he could convince CSH to get closer to each other. Striking is that HI is not with him. The moment he revealed his face to his coworkers, HI is never shown in the playground again. We can conclude that HI has already given up on JH, although she has not really admitted it. After the episode 4, HI only talks to JH at their office or at DC’s place. On the other hand, little by little CSH takes over. In the episode 9, she even goes there without him. In the episode 10, CSH even discovers that this playground is about to disappear. In the episode 11, we have this wonderful scene which represents the climax of their relationship.

As conclusion, the playground represents what grandfather Samuel told JH:

The playground is the place where CSH and JH’s love could start… If she hadn’t appeared there in the episode 2, I doubt that JH would have pursed her. That’s why we see the playground, when the preview for the next episode is shown.

Notice that there is no one… So CSH and JH might not be there any longer but when we see this place, we remember these scenes of JH and CSH there, especially the scene from the episode 16 which seals their love. The playground might disappear or change, yet their love will still exist.
Now, let us focus on the different meanings of the playground. A playground is a place where children go to play in order to have fun. And this is no coincidence that JH cherishes this place. This is linked to JH’s personality. JH’s favorite word is “fun”, he was always portrayed as a cheerful young man. Secondly, JH used the playground in order to spend time alone too. So this playground represents his secret place, where he can hide from others. Strangely, a playground is usually full with people therefore it is not really possible to hide. Yet, he goes there during the evening/night or if it is during the day, there is no one else there. Even if there was someone, I am sure, he had a book with him so that no one would approach him. Now, we can better understand why JH is using his smiles as a mask, he acts the same with the playground. This is his habit: hiding something in front of everyone. He doesn’t seclude himself where no one can see him. It is in the open air, he has an opposite behavior compared to JWS who goes to his room. Behind doors, our second lead can dwell on his feelings and thoughts.
Then if we pay attention to HI and JH’s interactions in the playground, we can see why from the second episode on, her one-sided love was doomed. In this scene, HI is chasing after JH who teased her just before calling her ugly.

Here, you can see on the one hand the playful nature of JH, on the other hand HI’s real position: HI has been waiting and chasing after JH but she was not able to catch his heart. So this scene symbolized their real position: HI will never be able to touch him and his heart. JH is not even aware of her feelings. He only has fun on his mind. Then later in the episode 3, both characters are sitting on the swing next to each other.

Neither JH goes to HI’s side, nor the latter approaches her friend. Both remain at the same distance which underlines once more that their relationship will never change. HI will never get closer to JH, but she will remain by his side. This is important because this illustrates that HI will never betray him.
Then if we take a look again at the scene where JH sees his boss for the first time at his playground, the viewer sees how CSH jumps off the swing as soon as JH calls her. Striking is that CSH chose to sit there before JH’s appearance. This outshines CSH’s sleeping playfulness. This is not visible yet. Then both remain standing close to the swings. Their position and their gesture reveal the gab between them. However, we can see the contrast to the scene in the episode 11:

Here, JH is kneeling in front of CSH. He left the swing and went to her side, touching her knee. This scene illustrates everything: CSH has accepted the playground as her treasure, she has already left the chaebol world. This metaphor comes true at the end of the episode 12. But JH’s kneeling in front of CSH embodies their respective status in the couple: for him, CSH is his princess. He is kneeling like the boy (credit to @Jemrie (forum soompi))

They have here the same position. Striking is that although CSH was considered as a princess due to her marriage with JWS, she was never treated as such in that terrible family. Neither JWS nor his mother treated her like a princess: she was either a maid or a doll. That’s why JWS bought her so many expensive gifts. He wanted to dress her up but the doll was always put in a certain place where people could admire her. Yet, it bothered him because the doll never reacted to his gifts. With JH, CSH’s cheerfulness has resurfaced, she likes being at the playground, she likes it, when JH pushes her gently… he brings movement and joy into her life. Then now, you must wonder why I came to think about JWS, while analyzing the playground. In my opinion, only when JWS sees JH and CSH interacting at the playground, he will realize that he has never treated CSH like a princess, that he has never known the real CSH. He never knew that she had a cheerful side, she could make jokes and tease her friends.
Remember that JWS only saw JH bringing CSH home with her car or he saw her at the hotel (episode 3) with JH, our second lead never witnessed how CSH would be in a different surrounding. CSH was always seen in his world with JH but never in JH’s surroudings.