Weeds can come up through the slats in your deck. In addition, these weeds can spread their seeds to your lawn where they can grow and ultimately overtake your lawn.
There are two primary ways to remove weeds from under your deck: chemical and non-chemical. Chemical options include applying a post-emergent herbicide, available at most home and garden stores. The advantage of this is that the weeds will be killed quickly and with relatively little labor. The downside is that herbicides are toxic and can be harmful if used incorrectly. Non-chemical options include hand pulling and using a gardening hoe. While more time intensive, these methods are safer.
To prevent weeds from growing under your deck in the future, lay down a black landscape fabric, available at most home and garden stores. Black landscape fabric prevents sunlight and water from reaching the soil, thus preventing weeds from growing.