They are one of the very few companies in that space which still develop their own search technology instead of just adopting and mixing available open source packages.
Most other search software these days runs on some flavour of Lucene and rightfully so IMO because Lucene is a rock solid piece of software.
This means that creating a defensible USP in that space isn't easy. Algolia did it by essentially developing their own search software from the ground up. It isn't necessarily better than competitors like Elasticsearch in every measure but it certainly has some interesting properties and it can be pretty fast, especially for things like autocomplete.
plus, from the reading I did, the founders have been working in the search space for a long time and really seem to know what they're doing.
Lucene is great, but, it does have limitations: tough to embed in non-JVM applications and poor support for tokenizing things like emojis are two immediate things that come to mind.
Elasticsearch is maybe my favorite data storage product in the last 15 years, but the Algolia folks have taken a different approach that is also quite interesting.
the lucene standard tokenizer doesn't offer support for tokenizing emojis: it strips them out. I'm not aware of any lucene tokenizer that does support emojis tokenization. This isn't a huge deal, as lucene is open source and tokenizers can be written, but I'm just highlighting it as a shortcoming that's illustrative of the time and place lucene evolved from.
This means that creating a defensible USP in that space isn't easy. Algolia did it by essentially developing their own search software from the ground up. It isn't necessarily better than competitors like Elasticsearch in every measure but it certainly has some interesting properties and it can be pretty fast, especially for things like autocomplete.