Worshipping together is one of the salient features Christianity which it shares with its predecessor Judaism and is followed by its successor Islam. Most of the religions have individualized worship experience. Worshippers visit shrines on their own to pray to their deity and does not necessarily need the company of others. However, gathering together for worship in the church, synagogue or the mosque is important for the above religions besides the private time of worship. So the two terms: "Personal worship" which signifies the individual's act of worship and "corporate worship" which is the worship which individuals offer in the company of other believers.
Some people are very keen on corporate worship but at the expense of the personal worship. They are regular at church services, praise and worship meetings etc but may not pour out their devotion and adoration to God when they are alone. These people find it difficult to meet God alone; they need the company of others. There are people on the other extreme who have a dislike to worship God in public, in the presence of others and they tend to be very private in their devotion and adoration of God. They are in the habit of shunning the gathering together of the saints in worship (Hebrews 10:25). They are very private persons and have a dislike for people.
However, both these extremes are certainly wrong. Personal time of worship and prayer is essential component of Christian spirituality. Jesus spent nights in praying alone. He taught that we should pray in secret (Mathew 6:6). He also went to the synagogues for corporate worship and the bible says it was his usual practice (Mark 10:1). This was the practice of the early church as well (Acts 2:42). They gathered together for fellowship, to receive apostles' teaching, prayer and breaking bread together besides their personal times of worship of God.
Personal worship and corporate worship are the two wings on which Christians soar to the presence of God in adoration and praise. They are two aspects of one act called worship: the creatures adoring the majesty of the creator, the sinners pouring out his their profound love for their saviour. Personal worship leads the worshipper to corporate worship because the worshippers have reached a level of adoration which they cannot hold within themselves any longer and need to get it out of their chest! So they look to corporate worship as a place where they can share it with others and to receive from people who have something to share. In a similar manner, the corporate worship should be so rich an experience that the worshipper leaves the place of worship to continue the worship at a personal level until another time for worship arrives. Personal worship propels people from their prayer closet to the chapel and the chapel is so compelling that they return to their closet to continue the worship. They are mutually enriching experiences.