On the face of it, the characteristics of transcendence and immanence appear to be in conflict. A transcendent God is one who is beyond perception, independent of the universe, and wholly other when compared to us. An immanent God, is one which exists within within us, within the universe, etc. and, hence, very much a part of our existence. How can these qualities exist simultaneously?
The idea of a transcendent God has roots both in Judaism and in Neoplatonic philosophy. The Old Testament, for example, records a prohibition against idols and this can be interpreted as an attempt to emphasize the wholly otherness of God which cannot be represented physically. Neoplatonic philosophy, in a similar manner, emphasized the idea that God is so pure and perfect that it completely transcended all of our categories, ideas, and concepts.
The idea of an immanent God can also be traced to both Judaism and Greek philosophers. The stories of the Old Testament depict a God who is very active in human affairs and the working of the universe. Christians, especially mystics, have often described a God who works within them and whose presence they can perceive immediately and personally. Philosophers have also discussed the idea of a God who is somehow united with our souls, such that this union can be understood and perceived by those who study and learn enough.
The idea of God being transcendent is very common when it comes to the mystical traditions within various religions. Mystics who seek a union or at least contact with God are seeking a transcendent God a God so totally other and so totally different from what we normally experience that a special mode of experience and perception is required.
Such a God is not immanent in our normal lives, otherwise mystical training and mystical experiences would not be necessary to learn about God. In fact, the mystical experiences are themselves generally described as transcendent and not amenable to the normal categories of thought and language which would allow those experiences to be communicated to others.
Clearly there is some conflict between these two characteristics. The more Gods transcendence is emphasized the less Gods immanence can be understood and vice-versa. For this reason, many philosophers have tried to downplay or even deny one attribute or the other. Kierkegaard, for example, focused primarily upon Gods transcendence and rejected Gods immanence this has been a common position for many modern theologians.
Moving in the other direction we find Protestant theologian Paul Tillich and those who have followed his example in describing God as our ultimate concern, such that we could not know God without participating in God. This is a very immanent God whose transcendence is ignored entirely if, indeed, such a God can be described as transcendent at all.
The need for both qualities can be seen in the other characteristics normally attributed to God. If God is a person and works within human history, then it would make little sense for us not to be able to perceive and communicate with God. Moreover, if God is infinite, then God must exist everywhere including within us and within the universe. Such a God must be immanent.
On the other hand, if God is absolutely perfect beyond all experience and understanding, then God must also be transcendent. If God is timeless (outside of time and space) and unchangable, then God cannot also be immanent within us, beings who are within time. Such a God must be wholly other, transcendent to everything we know.
Because both of these qualities follow readily from other qualities, it would be very difficult to abandon either without also needing to abandon or at least seriously modify many other common attributes of God. Some theologians and philosophers have been willing to make such a move, but most have not - and the result is a continuation of both of these attributes, constantly in tension.