Emacs displays the control characters 0 through 31 with a caret followed by another character. This convention dates back to the early teletype machines which were adopted by the first computers as input and output devices.
You can find out what ^L represents by looking at the table of ASCII characters:
Dec Hex Dec Hex Dec Hex Dec Hex Dec Hex Dec Hex Dec Hex Dec Hex
0 00 NUL 16 10 DLE 32 20 48 30 0 64 40 @ 80 50 P 96 60 ` 112 70 p
1 01 SOH 17 11 DC1 33 21 ! 49 31 1 65 41 A 81 51 Q 97 61 a 113 71 q
2 02 STX 18 12 DC2 34 22 " 50 32 2 66 42 B 82 52 R 98 62 b 114 72 r
3 03 ETX 19 13 DC3 35 23 # 51 33 3 67 43 C 83 53 S 99 63 c 115 73 s
4 04 EOT 20 14 DC4 36 24 $ 52 34 4 68 44 D 84 54 T 100 64 d 116 74 t
5 05 ENQ 21 15 NAK 37 25 % 53 35 5 69 45 E 85 55 U 101 65 e 117 75 u
6 06 ACK 22 16 SYN 38 26 & 54 36 6 70 46 F 86 56 V 102 66 f 118 76 v
7 07 BEL 23 17 ETB 39 27 ' 55 37 7 71 47 G 87 57 W 103 67 g 119 77 w
8 08 BS 24 18 CAN 40 28 ( 56 38 8 72 48 H 88 58 X 104 68 h 120 78 x
9 09 HT 25 19 EM 41 29 ) 57 39 9 73 49 I 89 59 Y 105 69 i 121 79 y
10 0A LF 26 1A SUB 42 2A * 58 3A : 74 4A J 90 5A Z 106 6A j 122 7A z
11 0B VT 27 1B ESC 43 2B + 59 3B ; 75 4B K 91 5B [ 107 6B k 123 7B {
12 0C FF 28 1C FS 44 2C , 60 3C < 76 4C L 92 5C \ 108 6C l 124 7C |
13 0D CR 29 1D GS 45 2D - 61 3D = 77 4D M 93 5D ] 109 6D m 125 7D }
14 0E SO 30 1E RS 46 2E . 62 3E > 78 4E N 94 5E ^ 110 6E n 126 7E ~
15 0F SI 31 1F US 47 2F / 63 3F ? 79 4F O 95 5F _ 111 6F o 127 7F DEL
Find the row with L in it, then read the corresponding character in the first column, which is FF, or Form Feed. The form-feed character caused the teletype to feed enough paper that it could be torn off below the current line, so most terminals simply clear the screen and return the cursor position to the origin when they see a ^L. This is probably the behavior that your program is expecting.
These characters also informed the default key bindings for Emacs and many other programs, which is why C-l is used for clearing or redrawing the screen in so many programs. It's also why C-h is used for backspace, and C-i for tab.
I'm sure you could implement something that examines incoming text and clears the current buffer when it sees a form-feed character. Or you could arrange to run this program inside term-mode
, which already implements this and many other terminal-like behaviors. You should be able to find instructions for that elsewhere.