strcpy has no way of knowing how large the destination buffer is (i.e. there is no length parameter) so sloppy programming using it can lead to overrunning the buffer and corrupting other memory. Such an overrun can lead to crashes, odd behaviour and may be exploitable by malware authors.
BTW, look at strncpy that takes a length parameter. One problem to be aware of is that strncpy will not terminate the string if the buffer is too small so it is dangerous in its own way.
In answer to your comment/question - it will depend on context. If you know the buffer is large enough (for example, you allocated it in the previous line at the correct size), use strcpy. If there is any possibility of an overflow then use strncpy and make sure you set the last position in the buffer to null. Note that "any possibility" should be interpreted very generously - unless the previous five or six lines are enough to show safety then use strncpy.
Also see Andon's comment above about strncpy_s. Finally, if you do use strcpy, you might want to add a #pragma to suppress the warning at that location.