Anmärkningsvärt means 'remarkably' or 'conspicuously', and can be broken down into two parts.
Anmärka means 'to remark on' or 'to observe', but has more critical connotations than its relative märka, which means 'to see/notice' in a neutral sense. Värt means 'worth' or 'worthy', so when you put the two together, you get an adverb to describe something that's 'worth making a few observations about'. It also exists in adjectival form: anmärkningsvärd/anmärkningsvärt depending on whether it defines an en or ett word).
Let's talk context. Anmärkningsvärt can be used in positive or neutral sense, like its synonym påfallande. For example, you could say that someone is an anmärkningsvärd person (an extraordinary person) or that they have done anmärkningsvärt bra arbete (remarkably good work).
But you will also hear it said with a chilly undertone, often implying that the speaker is surprised at someone else's incompetence, and inviting them to justify themselves. It belongs to a fairly formal register, so you'll hear it most often in situations where people need to be polite, replacing a word like dum (stupid) or konstig (strange) in situations where these words would be too rude and informal.
This means that a lot depends on tone, so if you read or hear a phrase such as 'Det är anmärkningsvärt att detta inte har hänt än' (it is remarkable that this hasn't happened yet) or 'Det finner jag anmärkningsvärt' (I find that remarkable), be aware that there may be a healthy does of passive aggression buried in the message.
For a real-world example, if you go to your communal laundry room and find a note from a neighbour (yes, Swedes enjoy leaving anonymous notes) saying they find it anmärkningsvärt that people keep forgetting to clean the fluff from the dryer filter, this isn't a mere musing on other people's laundry habits, but a Swedish speaker's way of letting you know they'd like the filter fluff-free.
Ingen har sett något anmärkningsvärt
No-one saw anything remarkable (In this case, anmärkningsvärt is used as an adjective)
Detta är ett anmärkningsvärt erkännande
This is a remarkable admission (In this example, anmärkningsvärt could be positive, neutral or critical, depending on the tone and context)