Filtered water is a broad category covering everything from a pitcher to a reverse osmosis system, and whether it is better for you depends entirely on what your water contained and what the filter is certified to remove. In many households the honest answer is that it tastes better and changes nothing else, which is a fair reason to do it.
Where the benefit is real
Where a test has found something and the filter is certified to reduce it. Lead from old plumbing, reduced by a certified carbon block or a membrane, is the clearest case. Nitrate on a well, reduced by reverse osmosis. Arsenic, by an appropriate medium. In each of those the filter is doing something measurable about a documented exposure, and the certification, confirmed in a certifier's listing rather than on a box, is what separates that from a hope.
Where it is comfort rather than health
On a monitored community supply meeting its requirements, a general carbon filter removes chlorine, which improves taste and smell and does not address a health risk, because the chlorine was doing a job and the utility's monitoring covers the rest. That is not a criticism: better tasting water means people drink more of it, and enjoying your tap water has a value even if it does not appear in a laboratory result. It is just worth knowing which you are buying.
The ways filtering can make things worse
Two, and both come from neglect rather than from filtering itself. A cartridge left in long past its rated volume stops working and, being warm and wet with trapped organics, can support bacterial growth. And removing the disinfectant residual means filtered water stored in a jug has nothing protecting it, so it should be refrigerated and used within a day or two rather than left standing. Neither is an argument against filtering; both are arguments for changing cartridges on schedule.
What filtering does not change
Hardness, unless the filter is a membrane, so scale and lather are unaffected by a carbon filter. The USGS describes hardness as dissolved calcium and magnesium, and they pass through carbon untouched. Nor does filtering add anything beneficial: water is not a significant source of minerals for someone eating normally, so neither removing nor retaining them moves the dial much. Our filtered shower head guide covers a related point of use question.
Questions people ask about is filtered water good for you
Is filtered water healthier than tap water?
Where a test found something the filter is certified to reduce, yes. On a monitored supply with no finding, it mainly tastes better.
Can filtering make water worse?
Only through neglect: a cartridge left past its capacity stops working and can support growth, and filtered water has no residual.
Does filtering remove beneficial minerals?
Carbon does not. Membranes do, though water is not a significant mineral source for someone eating normally.
Will a filter help with limescale?
No, unless it is a membrane treating that water. Hardness passes through carbon untouched.