The result (EAX) resides in the CPU in a format that INTEL calls "integer". You have first to extract the single decimal digits and then store them to an ASCII string which you can display. The usual method is to repeatedly divide the integer by 10 and store the remainder. Google for "assembly convert integer string" and you'll get a lot of exhaustive explanations.
This is your program doing it:
segment .data
    msg db "The sum is: "
    len equ $-msg
    lf db 0x0A
    number1 dd 7
    number2 dd 3
segment .bss
    sum resb 40                 ; 40 Bytes for an ASCII string
    sum_len resd 1
section .text
    global _start
_start:
    ; Addition
    mov eax, [number1]
    mov ebx, [number2]
    add eax, ebx
    ; Convert the number to a string
    mov edi, sum                ; Argument: Address of the target string
    call int2str                ; Get the digits of EAX and store it as ASCII
    sub edi, sum                ; EDI (pointer to the terminating NULL) - pointer to sum = length of the string
    mov [sum_len], edi
    ; Output "The sum is: "
    mov ecx, msg
    mov edx, len
    mov ebx, 1
    mov eax, 4
    int 0x80
    ; Output sum
    mov eax, 4
    mov ebx, 1
    mov ecx, sum
    mov edx, [sum_len]
    int 0x80
    ; Output Linefeed
    mov eax, 4
    mov ebx, 1
    mov ecx, lf
    mov edx, 1
    int 0x80
    ; Exit code
    mov eax, 1
    mov ebx, 0
    int 0x80
int2str:    ; Converts an positive integer in EAX to a string pointed to by EDI
    xor ecx, ecx
    mov ebx, 10
    .LL1:                   ; First loop: Save the remainders
    xor edx, edx            ; Clear EDX for div
    div ebx                 ; EDX:EAX/EBX -> EAX Remainder EDX
    push dx                 ; Save remainder
    inc ecx                 ; Increment push counter
    test eax, eax           ; Anything left to divide?
    jnz .LL1                ; Yes: loop once more
    .LL2:                   ; Second loop: Retrieve the remainders
    pop dx                  ; In DL is the value
    or dl, '0'              ; To ASCII
    mov [edi], dl           ; Save it to the string
    inc edi                 ; Increment the pointer to the string
    loop .LL2               ; Loop ECX times
    mov byte [edi], 0       ; Termination character
    ret                     ; RET: EDI points to the terminating NULL