According to Islamic sources, the Mahdi (Arabic: مهدي) is the ultimate saviour of humankind and the prophesied redeemer of the world. He is expected to emerge at near the end of times (i.e. before the Day of Judgment / Resurrection / Eschaton / in Arabic Yawm al-Qiyāmah يوم القيامة) to rule the world and to re-establish righteousness.
Generally speaking, the character of the Mahdi in Islam is very much similar to the Messiah in Judaism (known as Mashiach, in Hebrew: משיח). Both the Tanakh (Hebrew Bible) and the Talmud (the written version of the Jewish oral law) refer to Mashiach (משיח). It could be argued believing in the Mashiach is one of the Jewish principles of faith. Number 12 of 13 Jewish principles of faith formulated by Maimonides is as follows:
אני מאמין באמונה שלמה בביאת המשיח, ואף על פי שיתמהמה עם כל זה אחכה לו בכל יום שיבוא
I believe with perfect faith in the coming of the Mashiach; and even though he may tarry, nonetheless, I wait every day for his coming.
Praying for the arrival of the saviour (Mahdi in their language) is exactly what Shias do every day. Today is 15th of Shaban in Hijri calendar and so Shia Muslims across the world are celebrating their Imam Mahdi’s birthday and praying for his arrival. Watch these videos to get a sense of this Shia celebration: