Getting the gymnasts physically and mentally prepared at the start of a gymnastics session is important. General muscle stretching and joint articulation is mixed with a cardiovascular warm up and co-ordination exercises to get the brain warmed up too. This helps to get the gymnasts in the right mind frame for the session and improves their flexibility, which helps them learn their new gymnastics moves.
If gymnasts have done a long or intense session then a warm down at the end helps the muscles recover and limits muscle soreness in the following days. After a short session this is often not necessary.
The warm up and cool down also gives the coaches time to speak to the gymnasts and find out about any injuries or worries and to give feedback to the gymnasts at the end of the session.