Drupal- check if current page is taxonomy term page

You can use two solutions for this but avoiding the 2nd solution with arg() function is better according to Drupal docs. You should arg() function wherever possible because resulting code is hard to read.

1) Use menu_get_object function

$term = menu_get_object('taxonomy_term', 2);
if ($term) {
  // User is on a taxonomy term page
}

2) Use arg() function

if (arg(0) ==  "taxonomy" && arg(1) == "term" && is_numeric(arg(2)) && arg(3) == "") {
  // Taxonomy term page
}