It's reasonably effective, at least in my opinion. The HoL is definitely constitutionally weaker than the HoC, but because of (a) their influence (many are former politicians or other important figures) and (b) the delaying effect that repeatedly ping-ponging legislation between the houses has, if the House of Lords blocks something, then it often had a good chance of being amended at least partially to find a compromise.

In addition, the HoL gives people a place to criticize Government decisions with some authority - a lord complaining about a decision generally has more political influence than many other people (although in practice less political power).

There are some "loopholes" as it were - if a particular piece of legislation was part of the governing party's manifesto when they were elected (say, a government gets elected promising four day work weeks), then by convention, that legislation is passed through the HoL unchanged, on the basis that it has a clear democratic mandate. (It will still get discussed in both houses, and in the House of Commons, it'll get sent through a couple of rounds of cross-party committees to scrutinise the wording, so there are still some checks in place there.)

There are some flaws with the system. Firstly and most prominently, I suspect, in the eyes of the American observer: the House of Lords are unelected representatives. The word "Lords" in the name literally means what it says on the tin, and historically, many of the people sitting there were nobility who inherited their titles, and therefore were granted the right to sit there simply by birth. The New Labour reforms decreased the number of these peers to 92 (about an eighth of the around 750 peers currently active) and also added rules as to which people with hereditary titles would be able to claim those seats. In addition, the "Lords Spiritual" are a group of 25 seats set aside for bishops of the Church of England. The rest of the HoL operates more like the Supreme Court in the US, where someone will be given a lifetime peerage, generally as a reward for services to the country in some way. Many major former politicians therefore end up in the HoL, as do some campaigners or community organisers, as well as significant business leaders. Generally the government is and to choose who gets made a lord, although other parties are traditionally able to make suggestions to ensure that the makeup of the HoL stays reasonably fair, and isn't weighted too heavily to one party or another.

(As an aside, the non-bishop lords are known as the Lords Temporal, and if you enjoyed that fact, look up Black Rod, and the weird traditions that are associated with him.)

The other big criticism of the HoL is the size - the UK is I believe the only bicameral parliamentary system with an upper house larger than the lower house. This is because it's in every party's interest to stuff the House with more representatives for their party (or at least neutral representatives who can water down the opposition's strength). There are limits on how many new lords can be created, but I do not believe there's any limit on how big the HoL can become.

There are regularly discussions about how to "fix" the House of Lords - Labour fairly consistently have it as a manifesto promise, although how exactly they plan to reform the institution tends to change. A common suggestion is an elected house, but this has the effect that the upper house would look suspiciously like the lower house in terms of political makeup - most people who vote for one party in the House of Commons are unlikely to want a different party in the House of Lords. Alternatively, abolishing the Lords Spiritual and the hereditary peers is often proposed, but many Christians (or at least, people who see themselves as ethnically/culturally Christian) are opposed. In addition, the Lords Spiritual tends to lean left wing in the UK, regularly criticising the Government for failures in social policy such as food bank usage or lack of access to Universal Credit and other social security programs.

Personally, I'd like to see the Lords appointment process cleaned up - rather than being mainly a political decision, it would be good to have it entirely removed to either a cross-party group, or a separate group altogether. They would then be tasked with finding representatives from a wider range of candidates from the charity sector, arts, business, technology, and other places. The idea should be that the Lords represents more of a council of experts in a variety of fields. However, the principle of an unelected upper house that is strictly weaker than the lower house is not necessarily a bad one, and I think in recent years it has done a lot of good for the country.