Hey there,
嗨 has two meanings. The first, and I believe the original one is a direct translation of "hi" from English.
The second one, which is very popular at the moment in China, is like "excited" or "buzzing" or "having a great time in a place with an energetic atmosphere". It comes from the English for “high", as in the feeling after you take drugs high, but this is not what it means in Chinese, it just means that everybody was excited and buzzing and having a great time. I heard this all the time in China this summer. 起來 here just indicated that the process is starting. Everybody was starting to get really buzzing.
Laurence