"D-branes" can be described simply as boundary conditions in perturbative string theory. A D-brane is the place where superstrings can end. This can be shown by the diagram below:
In this example we have a D5-brane (shown in blue). This constitutes a slice of (hyper)space with the coordinates (x0,x1,x2,x3,x4,x5) where "x" is the particular dimension.
With superstrings propagating in ten dimensional spacetime (x0,x1,….,x9, ), in the case of the D5-brane, strings (shown as the curved lines) can end at a point in the (6 or higher dimensional space (x6-x9 on the diagram). That is, the string endpoints are anywhere in the six dimensional space-time.
The world-volume of a D5-brane is a five dimensional hyper-surface in the theory which propagates in time x0, thus defining a six dimensional space-time.
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