Itikaf imeans to spend time alone in the remembrance of ALLAH and to not mingle around with people until gets necessary. Itekaaf is observed in mosques. At the time of Muhammad s.a.w.w both male and females used to observe it in mosques because there are traditions that indicate the presence of the ummul mo’mineen in atikaaf with Muhammad s.a.w.w.
Coming back to Itikaf, it is that special worship in which a person leaves all the worldly things behind for 9 or 10 days and remembers ALLAH alone. This act of worship is only for ALLAH swt. The purpose of itekaaf is to seek guidance and to live alone for some days to be with our Creator only.
Being alone opens so many gates of wisdom and knowledge on us. it is a superlative degree of meditation in which a person feels that special and unknown peace which otherwise cannot be felt. Every person who observes it explains the same thing i.e. the peace and calmness of soul.
Before entering Itikaf, one must be in state of purity and his intentions should be only to worship ALLAH leaving all wordly affairs for some time. But this should also be noted that if there are parents or relations that need you, you should take care of them and if someone is there to help and look after the house mates, only then one can enter itekaaf. The running away from relationships is not what islam preaches and it is not liked.