Condition: jumps if CF = 1 or ZF = 1. After CMP a, b a borrow means a < b and a zero result means a = b; either one gives a ≤ b for unsigned numbers. It is the exact opposite of JA, which is why the two pair up when a jump has to be inverted.

Combined with a subtraction it gives a one-compare range test. Here the question is whether a character is an uppercase letter: after subtracting "A", the letters become 0..25 and everything else, including characters below "A" that wrap around, is larger.

Prints Y. Try "q" or "5": both print N.
MOV     AL, "Q"
SUB     AL, "A"        ; "A".."Z" become 0..25
CMP     AL, "Z" - "A"  ; 25
MOV     DL, "Y"        ; MOV leaves the flags alone
JBE     SHOW1          ; taken: DL stays "Y"
MOV     DL, "N"
SHOW1:
MOV     AH, 02h        ; DOS: print the character in DL
INT     21h

For signed values the matching jump is JLE. Use JBE for characters, counts, sizes and addresses.

Range

On the 8086 JBE exists only in the SHORT form: two bytes, opcode 76h and a signed 8-bit displacement counted from the end of the instruction. The target must lie within −128..+127 bytes of that point. To go farther, invert the test and hop over an unconditional JMP, which can reach the whole segment. MASM 6 makes this rewrite itself when it finds the target out of range (its default OPTION LJMP), so the listing may show two instructions where you wrote one.

JA      SKIP1    ; the opposite test, a short hop
JMP     FARAWAY  ; any distance in the segment
SKIP1:

Later CPUs

The 80386 added a near form of every conditional jump, 0Fh 86h followed by a 16-bit displacement (32-bit in 32-bit code), so from the 386 on JBE can reach anywhere in the segment. Code for the 8086 must stay with the short form.