Why Do We Have Gravity On Earth But Not In Space?

Because space is made up of gas and dust.

Actually, gravity is everywhere. But, this gravitational force depends on the product of the masses of the objects, which attract each other, and on the distance between them. The smaller the mass, the lower the attractive force. The larger the distance between the objects, the lower the attractive force (gravitational force decrease with the inverse square of the distance). Thus, the objects are more remote from another mass objects in the space than on Earth. Consequently, they are subjected to lower gravity.

The Earth's gravity comes from the mass of the Earth itself. Everything in the universe has gravity, some more and some less depending on size. Space is like an empty hole or area, so it doesn't have any weight, hence it has no gravity. If it did everything in the universe would be pulled together because of the enormity of it.