
ansprechen
to approach
To turn to someone in order to start a conversation.
Ein Fremder hat mich auf der Straße angesprochen und nach dem Weg gefragt.
A stranger approached me on the street and asked for directions.
to address / appeal to
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to approach
To turn to someone in order to start a conversation.
Ein Fremder hat mich auf der Straße angesprochen und nach dem Weg gefragt.
A stranger approached me on the street and asked for directions.

to address
To bring up a topic or problem and talk about it.
In der Besprechung müssen wir unbedingt das Budgetproblem ansprechen.
In the meeting, we absolutely have to address the budget problem.

to appeal to
To have a certain, usually positive, effect on someone; to please someone or spark their interest.
Das moderne Design des Stuhls spricht mich sehr an.
The chair's modern design really appeals to me.

to respond to
To react to a treatment or stimulus, especially in a medical context.
Der Patient spricht gut auf das neue Medikament an.
The patient is responding well to the new medication.
'Ansprechen' (to approach/address/appeal to) is a separable verb. The prefix 'an-' comes at the end in a main clause; in subordinate clauses and in the infinitive, it remains attached to the verb.
Warum sprichst du sie nicht einfach an?
Why don't you just approach her?
The object reveals the meaning: If you 'spricht man eine Person an' (approach a person), you start a conversation. If you 'spricht man ein Thema an' (address a topic), you talk about it. If a thing 'spricht eine Person an' (appeals to a person), they like it.
Er hat die neue Kollegin im Flur angesprochen.
He approached the new colleague in the hallway.
In the meaning of 'gefallen' (to please/appeal to), the thing that is pleasing is the subject of the sentence. The person who likes it is the accusative object.
Dieses Lied spricht mich emotional sehr an.
This song appeals to me very much emotionally.
In a medical context, 'ansprechen' (to respond) is almost always used with the preposition 'auf' and the accusative to describe a reaction to a treatment.
Die Entzündung spricht gut auf das Antibiotikum an.
The inflammation is responding well to the antibiotic.
to please / to fall
„Gefallen“ means that a design pleases someone and is perceived as pleasant. „Ansprechen“ emphasizes more that it sparks interest or has a particular effect; this does not yet have to mean that the person has made a final positive judgment. Choose „gefallen“ for a positive judgment and „ansprechen“ for the initial appeal.

Das schlichte Design spricht mich an und weckt mein Interesse.
The simple design appeals to me and sparks my interest.
Das schlichte Design gefällt mir sofort.
I immediately like the simple design.