The lens has a maximum magnification of 1:3.7, or 0.27 (augh, editing! The decimal number is created by dividing the first number by the last, and I got it super wrong) so it's really not that good a macro lens. By comparison, your current lens's maximum magnification is either 0.28 or 0.34 depending on whether it's the IS one or not, so it's actually higher.

So what that number means is that the image of the subject on the sensor (assuming a flat subject) is 0.27 times its actual size in real life. And the 550D's sensor is 22.3x14.9mm, so at the very closest, the smallest object you're going to be able to fill up the whole screen with will be those dimensions divided through by 0.27, or 82.5 x 55.1mm. Which is... about the size of a playing card, I think.

For more visual examples, I shot this (terrible) photo of ants and their larvae with a kit lens whose maximum magnification is about 1:4.5 (0.22). It is a crop - they were a bit smaller at full res. So that lens may be perfectly acceptable for your purposes if you're not going to go much farther than that. However, this picture of an ant (also a crop, but note the much higher detail) was taken with a specific-purpose macro lens (the Sigma 150mm f/2.8 macro), which has a 1:1 (1) maximum magnification.

'Proper' macro lenses usually have a maximum magnification similar to that of that lens; you can double the magnification on any of your lenses (at the cost of two stops of light) using a 2x extender/teleconverter like this one, but of course it depends on whether that two stops will be a problem, and what your budget is like.

Your camera has enough megapixels that if you're not shooting rapidly moving subjects and you're using a tripod or otherwise minimizing camera shake, you should be able to crop down to get decent pictures with your kit lens, more so than with that Tamron. But proper macro photography, as far as I know, does require a bit of an outlay for specialized equipment (and it will usually be a prime lens, not an ultrazoom like that one, that will have the magnification you need).