what is limiting line balmer series ? What does the above line mean?

The Balmer series is the light emitted when the electron moves from shell n to shell 2. So the lowest energy line is emitted in the transition from n = 3 to n = 2, the next line is from n = 4 to n = 2, and so on.

But the energy does not keep going up as you increase the value of n, because the energies of the orbitals (wrt the vaccum) tend to zero for large n. So as n \rightarrow \infty the energy released in moving from n nto 2 will tend to a finite limit. This is thelimiting line.

transition of electrons in orbits creates the limiting line of balmer series in uv region while other lines fall in visible region

Hey..! That`s damn simple limiting value of any series is n2= infinity.... As it has a finite value.....