I interpret your question to be asking for a description of 1-parameter groups of isometries.

The generic kind of motion in 3 dimensions is a screw-motion, which is translation along an axis combined with rotation about the same axis. Up to changing the speed of a parametrization, translations and rotations in 2 and 3 dimensions are all alike, but screw motions have an invariant, the pitch of the screw: how many complete turns are made with one unit of translation along the axis? Rotation is the limiting case pitch $\rightarrow 0$, while translation is the limiting case pitch $\rightarrow \infty$.

In 4 dimensions, in addition to rotations, translations and screw motions, there are compound rotations, which involve rotating about one 2-plane at one speed while rotating about the perpendicular plane at another speed. In 5 dimensions, there is also a compound screw-motion, which combines translation along a 1-dimensional axis with compound rotation in the perpendicular 4-plane.

The general pattern is similar. In dimension n, you can take any collection of mutually orthogonal 2-planes intersecting at a point and independently rotate each of them, and you can independently combine these rotations with translation in any direction that is a common perpendicular.