In synagogue life, it names an ascent to the Torah reading.
An aliyah is being called up to the Torah
Britannica explains that in the synagogue, aliyah refers to the honor of being called up to the bimah to recite blessings and, if able, participate in the Torah reading.
That is the meaning most relevant in liturgical life.
The word means ascent
Britannica notes that aliyah literally means "going up" or "ascent." In the synagogue this is enacted physically as the congregant goes up to the bimah.
That physical movement is part of the symbolism. Approaching the Torah is treated as an ascent toward something sacred.
The honor is structured and communal
Britannica describes how aliyot are distributed during Torah readings and how different services have different numbers of readings.
This matters because an aliyah is not spontaneous participation. It takes place inside a formal communal order.
Why it still matters
Aliyah still matters because it marks the public bond between an individual Jew and the Torah within the gathered community.
The shortest accurate answer
In synagogue worship, an aliyah is the honor of being called up to the bimah for the blessings and reading connected to the Torah service.