Here is an example of a certificate encoded in ASN.1 DER
30 82 01 8F 30 81 F9 **A0** 03 02 01 02 02 01 01 30
0D 06 09 2A 86 48 86 F7 0D 01 01 05 05 00 30 0D
31 0B 30 09 06 03 55 04 03 0C 02 43 41 30 20 17
0D 31 33 30 39 31 35 31 35 33 35 30 32 5A 18 0F
32 31 31 33 30 39 32 32 31 35 33 35 30 32 5A 30
0D 31 0B 30 09 06 03 55 04 03 0C 02 43 41 30 81
9F 30 0D 06 09 2A 86 48 86 F7 0D 01 01 01 05 00
03 81 8D 00 30 81 89 02 81 81 00 8D 80 B5 8E 80
8E 94 D1 04 03 6A 45 1A 54 5E 7E EE 6D 0C CB 0B
82 03 F1 7D C9 6F ED 52 02 B2 08 C3 48 D1 24 70
C3 50 C2 1C 40 BC B5 9D F8 E8 A8 41 16 7B 0B 34
1F 27 8D 32 2D 38 BA 18 A5 31 A9 E3 15 20 3D E4
0A DC D8 CD 42 B0 E3 66 53 85 21 7C 90 13 E9 F9
C9 26 5A F3 FF 8C A8 92 25 CD 23 08 69 F4 A2 F8
7B BF CD 45 E8 19 33 F1 AA E0 2B 92 31 22 34 60
27 2E D7 56 04 8B 1B 59 64 77 5F 02 03 01 00 01
30 0D 06 09 2A 86 48 86 F7 0D 01 01 05 05 00 03
81 81 00 0A 1C ED 77 F4 79 D5 EC 73 51 32 25 09
61 F7 00 C4 64 74 29 86 5B 67 F2 3D A9 39 34 6B
3C A9 92 B8 BF 07 13 0B A0 9B DF 41 E2 8A F6 D3
17 53 E1 BA 7F C0 D0 BC 10 B7 9B 63 4F 06 D0 7B
AC C6 FB CE 95 F7 8A 72 AA 10 EA B0 D1 6D 74 69
5E 20 68 5D 1A 66 28 C5 59 33 43 DB EE DA 00 80
99 5E DD 17 AC 43 36 1E D0 5B 06 0F 8C 6C 82 D3
BB 3E 2B A5 F1 94 FB 53 7B B0 54 22 6F F6 4C 18
1B 72 1C
What does the highlighted tag 0xA0 mean? What type it encodes?
The next value is 0x03 which is the length of the 0xA0 tag.
But the next byte after the length is actually INTEGER type - 0x02.
Who can explain this?
0xA0 is a Context Specific tag. In your example it contains an integer as you correctly deduced. In ASN.1 you can have 4 encoding of class of the 1-byte tag (more in section 8.1.2.2 of ITU-T X.690):
00xxxxxx)01xxxxxx)10xxxxxx)11xxxxxx)Personally I've never seen anything other than Universal (i.e sequence, integer, octet string) and context-specific.
You can explore the structure of the certificate by using ASN.1 Editor. I've selected the context specific tag here:

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