zeichnen
to draw
To create a picture or graphic representation with a pencil, chalk, or similar tool.
Sie kann sehr gut Porträts von Menschen zeichnen.
She can draw portraits of people very well.

to draw / sign
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to draw
To create a picture or graphic representation with a pencil, chalk, or similar tool.
Sie kann sehr gut Porträts von Menschen zeichnen.
She can draw portraits of people very well.

The verb 'zeichnen' (to draw/sign) is closely related to the noun 'das Zeichen' (sign/symbol). So 'zeichnen' literally means to create signs or lines. The result of this action is 'die Zeichnung' (the drawing).
Er machte ein Zeichen auf die Karte, um den Ort zu markieren.
He made a mark on the map to mark the place.
In the meaning 'erkennbar werden' (to become recognizable/apparent), the verb is reflexive: 'sich abzeichnen' (to become apparent). It is very often used in the impersonal phrase 'Es zeichnet sich ab, dass ...' (It is becoming apparent that ...) to describe a development or trend.
Es zeichnet sich ab, dass wir das Projekt rechtzeitig beenden werden.
It is becoming apparent that we will finish the project on time.
This meaning is used in the fixed passive construction 'gezeichnet sein von etwas' (to be marked by something). The 'von' (by) always introduces the cause of the negative traces, for example an illness, worries, or great effort.
Ihr Gesicht war von der langen Krankheit gezeichnet.
Her face was marked by the long illness.
In the basic meaning 'ein Bild erstellen' (to create a picture), 'zeichnen' (to draw) can be used with or without an object. The preposition 'mit' (with) is often used to name the tool.
Meine Tochter zeichnet gerne mit bunten Stiften.
My daughter likes drawing with colored pencils.
When 'zeichnen' is used in the sense of 'unterschreiben' (to sign), this is very formal and official language. It is found mainly in contracts, deeds, or historical documents.
Der Minister zeichnete das Abkommen im Namen der Regierung.
The minister signed the agreement on behalf of the government.
This meaning is limited to the field of finance. You can recognize it from signal words such as 'Aktien' (shares/stocks), 'Anleihen' (bonds), 'Investoren' (investors), or 'Börse' (stock exchange).
Die Anleger konnten die neuen Aktien für 50 Euro pro Stück zeichnen.
Investors were able to subscribe to the new shares for 50 euros each.
to buy
'kaufen' and 'zeichnen' can both relate to money and acquiring something. 'kaufen' is the normal word when you pay for something and receive it. In this context, 'zeichnen' has a special meaning in finance: you make a binding declaration that you want to buy shares or bonds at a certain price. So this is not drawing with a pen. The words can be confusing because the result is often a purchase. In everyday life, you almost always say 'kaufen'; for shares or bonds in an official offering, 'zeichnen' can be more precise.

Für den neuen Fonds können Anleger bis Freitag Anteile zeichnen.
Investors can subscribe to shares in the new fund until Friday.
Ihr kauft am Wochenende die Zugtickets für die Reise.
You are buying the train tickets for the trip this weekend.