What does "Swish" mean?

'swish' is just onomatopoeia for the ball not touching the rim, only the net as it goes through, making a swishing sound. It's not a noun or verb. It's the word for the sound it makes.

The implication of the word is that Sheldon did something really well, something without any flaws at all. It is not a common thing to say, but is immediately understandable.

Another similar thing to say with the same meaning is descriptive "nothing but net" (much more common).

Sheldon is using the phrase to celebrate his accuracy in guessing that there was awkwardness in the situation. Just as a basketball player makes a perfectly accurate shot, his comment was a particularly accurate reading of the situation. People use the expression "nailed it!" It a similar way. It's a very informal usage.

Other answers already covered the meaning: Sheldon is celebrating that he got it right. Not just right, but exactly right.

"Bullseye" would be another, very similar phrase used to denote getting something exactly right. However, "swish" is perhaps the more common (but still informal) phrase to use when congratulating oneself on a successful attempt at something, which is what Sheldon is doing.

Haven't watched the show, but I imagine he might also be pretending to throw a basketball as he says it. Whether or not he does, the metaphor is that he threw the ball (asked if he was correctly reading the situation), and not only did he score but he did so flawlessly, the ball going straight through the basket, making a "swish" sound.

In the gif below (from the show Futurama), the character Fry is similarly celebrating getting an answer right in class, though he was mostly just guessing.

Swish!