Accent
When a beat is accented, it carries a particular emphasis. There are three different types of rhythmic accent, all of which interact with each other.
Accent Types
Metric Accent
Metric accent is the emphasis intuitively felt in certain time signatures. For example, a measure of 4/4 often has emphases on the 1 and 3, so these would be called the "strong beats" or "on-beats". The metric accent is placed on them. The strongest beat of a measure (almost always the 1) is called the "crusis" or "downbeat", however the term "downbeat" has been used increasingly often to describe any strong beat.
Meanwhile, beats 2 and 4 are often considered "weak" beats. A weak beat is also called the "off-beat", and the weakest part of the beat is called the "anacrusis" or "upbeat" (however, "upbeat" is also used often to describe any weak beat). Many grooves start on the one-beat anacrusis and lead into the crusis. In this case, the anacrusis is referred to as a "pickup". For more information on why certain beats feel naturally accented, see this article on subjective rhythmization.
Dynamic Accent
Dynamic accent is the emphasis created by playing certain beats at louder volumes. Often, weak beats are dynamically accented (for example, the 2 and 4 in 4/4). When this occurs, the beat is called a backbeat. Dynamic accent is sometimes also referred to as "stress accent". Conversely, beats that are not dynamically accented are sometimes referred to as "unstressed".
Agogic Accent
Agogic accent is emphasis created by holding out a note for a longer period of time. Thus, it is not a purely rhythmic type of accent. It is also created by temporarily slowing down the tempo on a note, or pausing and playing the note late. For a more detailed description of the different types of agogic accent, visit this Wikipedia article.
Tonic Accent
Tonic accent is emphasis created by higher pitch. This type of accent is far more related to melody than rhythm, however there are still situations in grooves where it applies: For example, a triangle hit would have a tonic accent due to it's high pitch.
Notation
Since metric accent is intuitive, it is not notated. Tonic accent is just pitch, so it doesn't require any extra notation. Agogic accent is often represented by the length of a note, (Fermatas and caesuras can also be used) but it can also be used with dynamic accent in the symbols below:

Each of the above symbols carries a different meaning. From left to right:
- Staccato dot / staccato mark: This utilizes a mix of agogic and dynamic accent and signifies that the note should be played abruptly and short. Multiple staccato beats/notes should feel "disconnected". In jazz articulation, staccato is called "dit".
- Staccatissimo mark: This is an extreme version of staccato, meaning the beat/note should be played very abruptly and short.
- Marcato accent: A marcato beat/note is played short like staccato, but loudly like an accent mark. In jazz articulation, it is often called "daht".
- Accent mark: This utilizes dynamic accent and means that the note/beat should be played loudly, then taper off (as per the symbol shape). It does not alter the length of the note. In jazz articulation, it is called "dah".
- Tenuto mark: this uses agogic accent and means that the note should be smoothly held for its full length, or slightly longer, possibly even slowing the tempo (rubato). This is more related to notes than beats.