Itikaf means staying in the mosque (usually during the last 10 days of Ramadan) for a specific purpose which is to worship Allah.
Imam Al-Zuhri said: “How strange the Muslims are! They have given up Itikaf, despite the fact that the Prophet (peace be upon him) never abandoned this practice from the time he came to Madinah until his death.”
Itikaf offers an immense hidden benefit, which is protection from the effects of excessive socializing. Itikaf also offers protection from the evil consequences of talking and sleeping too much, because a person usually does Itikaf on his own, turning to Allah by praying Qiyamul-Layl (Night prayers), reading Quran, making Dhikr, reciting dua, and so on. Undoubtedly, a person’s success in freeing himself from excessive socializing, talking and sleeping, will help him to make his heart turn towards Allah, and will protect him from the opposite.
Imam Ibn Qayyim al-Jawziyyah says: "This leads him to feel contented with Allah instead of the people, which prepares him for being at peace with Him alone on the day of loneliness in the grave, when there is no one else to give comfort, nor anyone to grant solace except Him. So this is the greater goal of Itikaf."
Note: Women may also observe Itikaf at home. It was a constant practice of the wives of the Prophet Muhammad (peace be him and his wives).
"What is Itikaf and why is it important?" - Planet Arabic
Please note that there is a difference of opinion about women performing Itikaf at home. Islam QA states that it is not allowed for women to perform Itikaf at home whereas others are of the opinion that it can be done in women's case at home as noted here and here. Allah knows best.